Received February 17, 2012, in final form May 08, 2012; Published online May 11, 2012

Abstract
The Lie algebra $\mathfrak{su}(1,1)$ can be deformed by a reflection operator, in such a way that
the positive discrete series representations of $\mathfrak{su}(1,1)$ can be extended to representations
of this deformed algebra $\mathfrak{su}(1,1)_\gamma$.
Just as the positive discrete series representations of $\mathfrak{su}(1,1)$ can be used to model
a quantum oscillator with Meixner-Pollaczek polynomials as wave functions,
the corresponding representations of $\mathfrak{su}(1,1)_\gamma$ can be utilized to construct
models of a quantum oscillator.
In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials.
We study some properties of these wave functions, and illustrate some features in plots.
We also discuss some interesting limits and special cases of the obtained oscillator models.